Why we will say a cyclic quardilateral?

CBSE Class 10 Answered

Why we will say a cyclic quardilateral?

Asked by Rohit | 11 Jan, 2013, 09:02: AM

Expert Answer

If all the vertices of a quadrilateral lie on a circle, it is called as cyclic quadrilateral. That is, the quadrilateral is inscribed in a circle and all its vertices lie on the surface of the circle. A cyclic quadrilateral has some special properties which other quadrilaterals do not need to have.

i) The sum of either pair of opposite angles of a cyclic quadrilateral is 180⁰ .

ii) If one side of a cyclic quadrilateral is produced, then the exterior angle is equal to the interior opposite angle.

iii) If two opposite sides of a cyclic quadrilateral are equal, then the other two sides are parallel.

iv) The quadrilateral formed by angle bisectors of a cycle quadrilateral is also cyclic.

v) If two sides of a cyclic quadrilateral are parallel, prove that the remaining two sides are equal and the diagonals are also equal.

vi) An isosceles trapezium is always cyclic.

vii) If the bisectors of the opposite angles P and R of a cyclic quadrilateral PQRS intersect the corresponding circled at A and B respectively, then AB is diameter circle.

viii) The sum of the angles in the four segments exterior to a cyclic quadrilateral is equal to 6 right angles.

Answered by | 11 Jan, 2013, 09:16: AM